Time Dilation

What is time dilation?

An atomic clock is placed in a jet aeroplane. The clock measures a time interval of $3600 \mathrm{s}$, when the jet moves with speed $400 \raisebox{1ex}{$\mathrm{m} $}\!\left/ \!\raisebox{-1ex}{$\sec $}\right.$. How much larger a time interval does an identical clock held by an observer at rest on the ground measure?

Determine the relativistic time, if ${\mathrm{T}}_{\mathrm{o}}$ is $7$ years and the velocity of the object is $0.55 \mathrm{C}$.

A certain particle called $\mathrm{\mu }-$mesons has lifetime of $2\times {10}^{-6}\sec$. What is the mean lifetime when the particle is travelling with a speed of $2.944\times {10}^{10} \raisebox{1ex}{$\mathrm{cm}$}\!\left/ \!\raisebox{-1ex}{$\sec $}\right.$. How for it goes during one mean life?

A particle is travelling through the Earth's at morpheme at a speed of$0.866\mathrm{C}$. To an earth-bound observer, the distance. It travels $2.50 \mathrm{km}$. How for does the particle travel in the particle frame of reference?

Amount of by which measured time interval is greater than corresponding proper time interval is called:

A frame of reference has four coordinates $\mathrm{x}, \mathrm{y}, \mathrm{z}$ and $\mathrm{t}$ is referred to as the________.

Suppose a cosmic ray colliding with a nucleus in the Earth’s upper atmosphere produces a muon that has a velocity $\mathrm{v} = 0.950\mathrm{c}$. The muon then travels at constant velocity and lives $1.52 \mathrm{\mu s}$ as measured in the muon’s frame of reference. (You can imagine this as the muon’s internal clock.) How long does the muon live as measured by an Earth-bound observer?

A certain particle called $\mathrm{\pi }=$mesons is travelling with a speed of $60\%$ of the velocity of light. If it has a lifetime of $4\times {10}^{-6}\sec$. How for it goes during one mean life?

What is the dilation factor of a muon travelling with a velocity of $80\%$ that of the velocity of light?

Two babies are born in a moving train, one in the compartment adjacent to the engine and other in the compartment adjacent to the guard. According to the train frame, the babies are born at the same instant of time. Who is elder according to the ground frame ?

A person travels by a car at a speed of $180 \mathrm{km}/\mathrm{h}$. It takes exactly $10 \mathrm{hours}$ by his wristwatch to go from the station A to the station B. Calculate the difference between time taken in the road frame by the car to go from the station A to the station B and the time measured by wristwatch.

A clock keeps correct time on earth. It is put in a space-ship travelling with velocity $\frac{c}{2}$. If the number of hours it loses in a day are $24-x\sqrt{3}$. Find $x$.

The half-life of a $\pi -\mathrm{meson}$ at rest is $4.2\times {10}^{-6} \mathrm{seconds}.$ Its half-life when it will travel with the speed of $c/4$ is _____$\times {10}^{-6} \mathrm{s}$. (Approximate up to two decimal places)